Vth using Node
In using Node
Rth or Rn
Finding Rth using source injection and node
Here is the mupad/matlab code that generates the answer Rth = 6.0591 ohms.
Comparing Node with Thevenin Equivalent
Solving the node equations yields:
Using the Thevenin equivalent (and voltage divider) to compute voltage across the 12 ohm resistor:
So they match ...
Thevenin voltage and resistance can not be computed from a node analysis of the entire circuit, but the node analysis of the entire circuit can be used to check if the thevenin equivalent produces the same numbers.